Displacement using UV map affecting all maps, not just the one selected
When you create a second UV map in Blender, the operator (or better said, the + Button in the Mesh Data / UV Maps Panel) will create a COPY of the currently active UV map. If you rethink the steps you made, what happened is that you copied the UV map you created in the steps 1-5, and you cannot get rid of already unwrapped faces. And that's why you get the effect on both faces in step 12, you basically really have a UV map containing both sides of the Cube.

Try this: Start off with creating two UV maps on a new Cube as step number 1.  But make sure you create the UV map while in edit mode and no vertex or face selected! This will create a UV map where all UVs have the coordinates (0, 0). then do the unwrapping part for both of them as you did in your description. That should ensure that both UV maps are "totally empty" when you dig into the details.